Property:Abstract
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A
This paper presents the use of pulsed air injection to control the onset of rotating
stall in a low-speed, axial flow compressor. By measuring the unsteady pressures near the
rotor face, a control algorithm determines the magnitude and phase of the first mode of
rotating stall and controls the injection of air in the front of the rotor face.
Experimental results show that this technique slightly extends the stall point of the
compressor and eliminates the hysteresis loop normally associated with rotating stall. A
parametric study is used to determine the optimal control parameters for suppression of
stall. Analytic results---using a low-dimensional model developed by Moore and Greitzer
combined with an unsteady shift in the compressor characteristic to model the
injectors---give further insights into the operation of the controller. Based on this
model, we show that the behavior of the experiment can be explained as a change in the
bifurcation behavior of the system under nonlinear feedback. A higher fidelity simulation
model is then used to further verify some of the specific performance characteristics that
are observed in experiments. +
T
This paper proposes a method of improving per- formance of scalar discrete-time systems with substantial delay by adding additional delayed feedback channels (i.e. imposing a distributed delay feedback). The optimal weights for the added feedback channels are found using optimization techniques. In particular, we reduce the H1 norm of the closed loop transfer function with multiple delayed feedback using techniques from static output feedback design. We impose constraints on the feedback gain in order to highlight the effectiveness of the distribution. In this manner, improvement on performance is a result of the distribution and not a change in the overall effective gain. The concept of applying a multiple delayed feedback channel is inspired by biological systems, where substantial delays can be present in feedback control. To show the effectiveness of this idea we apply our method to an example of a scalar genetic autoregulatory network. The constraint on the gain allows one to implement the feedback in a genetic regulatory network without having to change the reaction rates. A possible method of synthesizing such a system in a wet lab is explained in more detail. Finally, stability results indicate the possibility of stabilizing an unstable system with added delayed feedbacks (by adding larger delays). This approach may also be applicable to systems with large delays in which simple controllers are needed due to limitations in computational power. This paper motivates and provides preliminary results towards direct design of purely delay based controllers for network systems with large delays. +
F
Feasible Trajectories of Linear Dynamic Systems with Inequality Constraints Using Higher-Order Representations +
This paper proposes a method to determine trajectories of dynamic systems that steer
between two end points while satisfying linear inequality constraints arising from limits
on states and inputs. The method exploits the structure of the dynamic system written in a
higher-order form to explicitly eliminate the state equations. The feasible trajectories
of the dynamic system are sought within a characterization with a finite sum of mode
functions. In this paper, the linear inequalities on inputs and states are replaced by a
finite set of linear inequalities on the mode coefficients. This step changes the problem
of trajectory generation into finding a convex polytope enclosed by the linear
inequalities on the mode coefficients. A procedure is then developed to efficiently find
the vertices of this bounding polytope. It is demonstrated in this paper that this method
can generate feasible trajectories of the system in real-time and can quickly update the
trajectories as the terminal conditions are changed. The procedure is demonstrated
numerically by two examples. The results of one of the examples is implemented in hardware
to explore the issues of real-time planning and control. +
D
This paper proposes a new synthetic in vitro circuit that aims at regulating the rate of RNA transcription through positive feedback interactions. This design is dual to a previously synthesized transcriptional rate regulator based on self-repression. Two DNA templates are designed to interact through their transcripts, creating cross activating feedback loops that will equate their transcription rates at steady state. A mathematical model is developed for this circuit, consisting of a set of ODEs derived from the mass action laws and Michaelis--Menten kinetics involving all the present chemical species. This circuit is then compared to its regulatory counterpart based on negative feedback. A global sensitivity analysis reveals the fundamental features of the two designs, by evaluating their equilibrium response to changes in the most crucial parameters of the system. +
Differentially Flat Systems with Inequality Constraints: An Approach to Real-Time Feasible Trajectory Generation +
This paper proposes a real-time planning scheme and its implementation for a class of dynamic systems. The planner is aimed to satisfy the state equations, the path and actuator constriants, and the given initial and terminal constraints. In order to generate trajectories in real-time, three broad steps are performed: (1) the structure of differentially flat systems is used to explicitly encapsulate the state equations into linear differential constraints in a flat space, and appropriately transform the boundary conditions; (ii) using semi-infinite optimization theory, an inner approximation of nonlinear constraints is made to replace these by a set of linear inequalities in the flat space, i.e., by a polytope; (iii) this polytopic representation of the system that satisfies the state equations and the constraints is then parameterized using basis functions and the planning problem is turned around into solution of a set of linear inequalities in the coefficient space of the basis functions. It is then demonstrated that numerically efficient algorithms can be built to solve the planning problem in real-time. The essence of the approach is demonstrated by two examples: (1) an implementation is performed on a spring-mass-damper system to demonstrate the real-time capability of evasion-pursuit; (ii) a VTOL aircraft is used to illustrate the application of this approach in simulation to nonlinear problems. +
A
This paper proposes a set-based parameter identi- fication method for biochemical systems. The developed method identifies not a single parameter but a set of parameters that all explains time-series experimental data, enabling the systematic characterization of the uncertainty of identified parameters. Our key idea is to use a state-space realization that has the same input-output behavior as experimental data instead of the experimental data itself for the identification. This allows us to relax the originally nonlinear identification problem to an LMI feasibility problem validating the norm bound of an error system. We show that regions of parameters can be efficiently classified into consistent and inconsistent parameter sets by combining the LMI feasibility problems and a generalized bisection algorithm. +
N
This paper proposes an intuitive nonlinear lateral control strategy for trajectory tracking in autonomous
nonholonomic vehicles. The controller has been implemented and verified in Alice, Team Caltech's contribution to the 2007 DARPA Urban Challenge competition for autonomous
motorcars. A kinematic model is derived. The control law is described and analyzed. Results from simulations and field tests are given and evaluated. Finally, the key features of the proposed controller are reviewed, followed by a discussion of some limitations of the proposed strategy. +
E
Evaluation Metrics of Object Detection for Quantitative System-Level Analysis of Autonomous Systems +
This paper proposes two new metrics to evalu- ate learned object detection models for quantitative system-level analysis via probabilistic model-checking. In particular, proposition-labeled and distance-parametrized confusion matrices are defined for evaluating object detection, and these metrics are leveraged to compute the probability of the closed- loop system satisfying its system-level formal specifications. Instead of using object class labels, the proposition-labeled confusion matrix uses atomic propositions relevant to the high- level planning strategy. Furthermore, unlike the traditional confusion matrix, the distance-parametrized confusion matrix accounts for variations in detection performance with respect to the distance between the ego and the object. We empirically show that these evaluation metrics chosen with the context of i) system-level specifications and ii) the planning module lead to a less conservative analysis in comparison to canonical metrics that do not take these into account. We demonstrate this framework on a discrete-state car-pedestrian example by computing the satisfaction probabilities for safety requirements formalized in Linear Temporal Logic (LTL). +
C
This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations. +
E
This paper provides analytical results regarding the stability of linear discrete-time systems with stochastic delays. Necessary and sufficient stability conditions are derived by using the second moment dynamics which can be used to draw stability charts. The results are applied to a simple connected vehicle system where the stability regions are com- pared to those given by the mean dynamics. Our results reveal some fundamental limitations of connected cruise control which becomes more significant as the packet drop ratio increases. +
A
Analysis of Delays in Transcriptional Signaling Networks with Time-Varying Temperature-Dependent Rate Coefficients +
This paper provides preliminary work in an aim to fundamentally understand the effects of temperature fluctuations in the dynamics of biological oscillators. Motivated by circadian rhythms, we are interested in understanding how time-varying temperatures might play a role in the properties of biochemical oscillators. This paper investigates time-dependent Arrhenius scaling of biochemical networks with delays. We assume these time-delays arise from a sequence of simpler reactions that can be modeled as an aggregate delay. We focus on a model system, the Goodwin oscillator, in which we use time-varying rate coefficients as a mechanism to understand the possible effects of temperature fluctuations. The emergence of delays from a sequence of reactions can be better understood through the Goodwin model. For a high order system and comparably high reaction rates, one can approximate the large sequence of reactions in the model with a delay, which can be interpreted as the time needed to go through the âqueueâ. Such types of delays can arise in the process of transcription for example. To study how these delays are affected by temperature fluctuations, we take the limit as the order of the system and the mean reaction rates approach infinity with a periodically time-varying rate coefficient. We show that the limit cycle of the Goodwin oscillator varies only in the limit when the oscillator frequency is much larger than the frequency of temperature oscillations. Otherwise, the instantaneous frequency of the oscillator is dominated by the mean value of the time-varying temperature. +
E
This paper studies the evaluation of learning- based object detection models in conjunction with model-checking of formal specifications defined on an abstract model of an autonomous system and its environment. In particular, we define two metrics – proposition-labeled and class-labeled confusion matrices – for evaluating object detection, and we incorporate these metrics to compute the satisfaction probability of system-level safety requirements. While confusion matrices have been effective for comparative evaluation of classification and object detection models, our framework fills two key gaps. First, we relate the performance of object detection to formal requirements defined over downstream high-level planning tasks. In particular, we provide empirical results that show that the choice of a good object detection algorithm, with respect to formal requirements on the overall system, significantly depends on the downstream planning and control design. Secondly, unlike the traditional confusion matrix, our metrics account for variations in performance with respect to the distance between the ego and the object being detected. We demonstrate this framework on a car-pedestrian example by computing the satisfaction probabilities for safety requirements formalized in Linear Temporal Logic (LTL). +
F
This paper summarizes the findings and recommendations of a recent panel on
Future Directions in Control, Dynamics, and Systems, sponsored by the US Air
Force Office of Scientific Research. A set of grand challenges that
illustrate some of the recommendations and opportunities are provided.
Finally, the paper describes two new courses being developed at Caltech that
are aligned with the recommendations of the report. +
S
This report describes Team Caltech's technical approach and results for the 2007 DARPA Urban Challenge. Our primary technical thrusts were in three areas: (1) mission and contingency management for autonomous systems; (2) distributed sensor fusion, mapping and situational awareness; and (3) optimization-based guidance, navigation and control. Our autonomous vehicle, Alice, demonstrated new capabiliites in each of these areas and drove approximately 300 autonomous miles in preparation for the race. The vehicle completed 2 of the 3 qualification tests, but did not ultimately qualify for the race due to poor performance in the merging tests at the National Qualifying
Event. +
L
This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the performance of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems. +
A
This report presents techniques for using discrete finite
rotations to reorient a spacecraft from a given initial attitude to a
final attitude which satisfies a specified aiming objective. The
objective may be a fully specified final orientation or it may require
that the spacecraft direct an instrument along a certain
direction. Constraints are also imposed on the allowable intermediate
orientations that the spacecraft may assume during the course of the
maneuver, representing the operational requirements of onboard
instrumentation. The algorithms presented consider solutions that
will achieve the desired objective with only one or two slew
maneuvers, although they may be easily extended to consider more
complicated solutions requiring additional maneuvers. +
O
This research addresses the path planning problem
with a nonlinear optimization method running in real
time. An optimization problem is continually solved to find a
time-optimal, dynamically feasible trajectory from the vehicleâs
position to some receding horizon ahead (20m-70m forward).
The locally optimal numerical solver optimizes both the spatial
and temporal components of the trajectory simultaneously, and
feeds its output to a trajectory-following controller. The method
has been implemented and tested on a modified Ford E350
van. Using one stereo pair and four LADAR units as terrain
sensors, the vehicle was able to consistently traverse a 2 mile
obstacle course at the DGC qualifying event. At the main
DGC event, the vehicle drove 8 autonomous miles through the
Nevada desert before experiencing non-planning issues. During
this time, the planning system generated a plan 4.28 times
per second on average. This execution speed, coupled with a
feedback-based trajectory-following controller was shown to be
adequate at providing smooth and reliable obstacle avoidance
even on complicated terrain. +
C
Control Theory for Synthetic Biology: Recent Advances in System Characterization, Control Design, and Controller Implementation for Synthetic Biology +
This survey aims to provide a general overview of relevant terms and resources for understanding the intersection of synthetic biology and control theory. A reader with a background in control theory should come away with a reasonable understanding of the current 24 state-of-the-art of biological system identification, controller design and implementation, and the open challenges facing the field. Additionally, this review updates and builds upon previous publications on this subject. As this particular work is limited to a selected number of topics, additional reviews are suggested throughout the text for deeper reading. In the following sections, each of the challenges is addressed within the typical workflow for control implementation of more traditionally engineered systems (Figure 1). Engineered biological systems present a number of challenges to all stages of this workflow for reasons such as limitations in real-time measurement, resource competition with the host organism, and incomplete knowledge of underlying biological processes. First, strategies for framing a biologi- cal organism as a system with defined inputs, outputs, sensors, actuators, and measurements are discussed (Figure 1a). Obtaining dynamic and reliable measurements within biological organisms is a daunting challenge, engineered or otherwise. An overview of the state-of-the-art tools for modeling and characterizing biological systems is presented, followed by system identification methods specifically designed for the types of data available from biological measurements. The difficulty in engineering complex genetic networks, combined with severe limitations in real- time measurement, means that the body of work for controller design (Figure 1b) is limited – as a result, we discuss the open problems and challenges awaiting the entrepreneurial reader, and also present a number of examples of feedback loop implementation in living cells (Figure 1c). Finally, the necessary challenges in synthetic biology and development of control theoretical frameworks that need to be addressed in order to advance the field are discussed.
S
This thesis addresses the problem of estimating the state in multi-agent decision and
control systems. In particular, a novel approach to state estimation is developed that uses
partial order theory in order to overcome some of the severe computational complexity
issues arising in multi-agent systems. Within this approach, state estimation algorithms are
developed, which enjoy proved convergence properties and are scalable with the number
of agents.
<p>
The dynamic evolution of the systems under study are characterized by the interplay of
continuous and discrete variables. Continuous variables usually represent physical quan-
tities such as position, velocity, voltage, and current, while the discrete variables usually
represent quantities internal to the decision protocol that is used for coordination, com-
munication, and control. Within the proposed state estimation approach, the estimation of
continuous and discrete variables is developed in the same mathematical framework, as a
joint continuous-discrete space is considered for the estimator. This way, the dichotomy
between the continuous and discrete world is overcome for the purpose of state estimation.
<p>
Application examples are considered, which include the state estimation in competi-
tive multi-robot systems and in multi-agent discrete event systems, and the monitoring of
distributed environments. +
T
This thesis explores the paradigm of two degree of freedom design for
nonlinear control systems. In two degree of freedom design one
generates an explicit trajectory for state and input around which the
system is linearized. Linear techniques are then used to stabilize the
system around the nominal trajectory and to deal with
uncertainty. This approach allows the use of the wealth of tools in
linear control theory to stabilize a system in the face of
uncertainty, while exploiting the nonlinearities to increase
performance. Indeed, this thesis shows through simulations and
experiments that the generation of a nominal trajectory allows more
aggressive tracking in mechanical systems.
<p>
The generation of trajectories for general systems involves the
solution of two point boundary value problems which are hard to solve
numerically. For the special class of differentially flat systems
there exists a unique correspondence between trajectories in the
output space and the full state and input space. This allows us to
generate trajectories in the lower dimensional output space where we
don't have differential constraints, and subsequently map these to the
full state and input space through an algebraic procedure. No
differential equations have to be solved in this process. This thesis
gives a definition of differential flatness in terms of differential
geometry, and proves some properties of flat systems. In particular,
it is shown that differential flatness is equivalent to dynamic
feedback linearizability in an open and dense set.
<p>
This dissertation focuses on differentially flat systems. We describe
some interesting trajectory generation problems for these systems, and
present software to solve them. We also present algorithms and
software for real time trajectory generation, that allow a
computational tradeoff between stability and performance. We prove
convergence for a rather general class of desired trajectories. If a
system is not differentially flat we can approximate it with a
differentially flat system, and extend the techniques for flat
systems. The various extensions for approximately flat systems are
validated in simulation and experiments on a thrust vectored
aircraft. A system may exhibit a two layer structure where the outer
layer is a flat system, and the inner system is not. We call this
structure \emph{outer flatness}. We investigate trajectory generation
for these systems and present theorems on the type of tracking we can
achieve. We validate the outer flatness approach on a model helicopter
in simulations and experiment.
